It should not be thought that the air near the surface of the earth, which we breathe, has its natural extension: for since that which is above is heavy and has the power of a spring, that which is here below, being loaded with the weight of the whole atmosphere, ought to be much more condensed than that which is higher up, which is free to dilate; and that which is between the two extremes ought to be less condensed than that which is on the earth and less dilated than that which is the most remote.
We can understand in a way this difference of condensation of air by using the example of many sponges, which have been piled one on the other. For it is evident that those which are at the top of the pile will have their natural extent; that those which are just below them will be a little less dilated; and that those which are at the bottom of the whole pile will be very closely compressed and condensed. It is further plain that, if we take away all those at the top, those below will recover their natural extent by the power of the spring which they have, and that if we take away only a part they will recover only a part of their dilation.
The first question that we can ask is to know if the air condenses itself precisely in the proportion of the weights with which it is loaded, or if this condensation follows other laws and of the proportions. I give here the steps of the argument which I used to determine whether the condensation of air is in proportion to the weights which compress it.
If we suppose, as experiment shows, that air condenses more when it is compressed by a greater weight, it necessarily follows that if the air, which extends from the surface of the earth to the greatest height at which it terminates, becomes lighter, the lowest part of it would be more dilated than it is at present, and if it becomes heavier this same part would be more condensed. We must therefore conclude that the condensation which it has near the earth is in a certain proportion to the weight of the air above it by which it is compressed, and that in this condition it is precisely in equilibrium by its spring with the whole weight of the air which it sustains.
From which it follows that if we introduce some air along with the mercury of a barometer and perform the experiment of the vacuum, the mercury will not remain in the tube at its ordinary height: for the air which is enclosed in it before the experiment makes equilibrium by its spring with the weight of the whole atmosphere, that is to say, with the column of air of the same section which extends from the surface of the mercury of the vessel to the limits of the atmosphere, and consequently, since the mercury which is in the tube encounters nothing which makes equilibrium with it, it will descend, but it will not descend altogether; for when it descends the air enclosed in the tube dilates, and consequently its spring is no longer sufficient to make equilibrium with all the weight of the air above it. Therefore a part of the mercury must remain in the tube at such a height that, since the air which is enclosed is in a condition of condensation which gives it a force of spring that can sustain only a part of the weight of the atmosphere, the mercury which remains in the tube makes equilibrium with the rest, and then there will be equilibrium between the weight of the whole column of air and the weight of the remaining mercury joined to the force of the spring of the enclosed air. Now if the air is condensed in proportion to the weight with which it is loaded, it follows necessarily that if we make an experiment in which the mercury remains in the tube at the height of fourteen inches, the air which is enclosed in the rest of the tube will be then dilated twice as much as it was before the experiment; provided that at the same time in the barometers without air the mercury is raised precisely to twenty-eight inches.
To determine if this conclusion was the true one I carried out experiments with M. Hubin, who is very expert in constructing barometers and thermometers of many sorts. We used a tube forty inches long, which I had filled with mercury up to twenty-seven inches and a half, so that there were twelve and a half inches of air, and when it was immersed by an inch in the mercury of the vessel, there were thirty-nine inches remaining to contain fourteen inches of mercury and twenty-five inches of air expanded to twice its original volume. I was not deceived in my expectations: for when the end of the inverted tube was plunged in the mercury of the vessel, the mercury of the tube descended and after some oscillations stood quiet at a height of fourteen inches; and consequently the enclosed air, which then occupied twenty-five inches, was extended to double the volume of that which had been enclosed in the tube when it occupied only twelve and a half inches.
I had him make another experiment in which he left twenty-four inches of air above the mercury and the mercury descended to seven inches, in agreement with this hypothesis; for seven inches of mercury made equilibrium with a quarter of the weight of the whole atmosphere and the three quarters which remained were sustained by the spring of the enclosed air, which then being extended to thirty-two inches was in the same ratio with its original extent of twenty-four inches as the entire weight of the air is to three quarters of the same weight.
I had him try some other similar experiments, in which more or less air was left in the same tube or in others of different sizes; and I always found that when the experiment was tried the proportion of the dilated air to the extent of that which had been left above the mercury before the experiment was the same as that of twenty-eight inches of mercury, which is the whole weight of the atmosphere, to the difference between twenty-eight inches and the height at which the mercury stood after the experiment: and thus it is made sufficiently clear that we can take as a fixed rule or law of nature that air is condensed in proportion to the weight with which it is loaded.
If we wish to make more delicate experiments we must have a recurved tube, of which the two branches are parallel, one of which is about eight feet long and the other twelve inches; the long tube ought to be open at the top and the other carefully sealed.
We begin by pouring in a little mercury to fill up the bottom where the two branches communicate, and we arrange it so that the mercury stands no higher in one than in the other, so as to be assured that the enclosed air is neither more condensed nor more dilated than the free air.
We then pour mercury into the tube little by little, taking care that the shock does not introduce any additional air into that which is enclosed, and we shall see, as I have seen several times, that when the mercury in the other will be fourteen inches higher, that is to say eighteen inches above the communicating tube; which is what ought to happen if air condenses in proportion to the weight with which it is loaded; since the enclosed air is then loaded with the weight of the atmosphere, which is equal to the weight of twenty-eight inches of mercury, and also with that of fourteen inches, of which the sum 42 inches is to 28 inches, the first weight which kept the air at twelve inches in the small branch, reciprocally as this extent of twelve inches is to the remaining extent of eight inches.
If we again pour in mercury until it rises to 6 inches in the small branch, so that there remains only 6 inches of air, the mercury in the other branch will be higher by 28 inches than the height of these six inches; which is what ought to happen according to the same hypothesis: for then the enclosed air will be loaded with 28 inches of mercury and with the weight of the atmosphere, which is also 28, the sum of which 56 is twice 28 as the first extent of 12 inches of air is twice that of the 6 inches which remain; and when as we continue to pour mercury into the long branch it rises in the small branch to a height of 8 inches, there will be 56 inches of mercury above it in the long branch, which makes again the same proportion.
If we wish to carry the experiment further we may pour in still more mercury, until the air in the small branch is reduced to 3 inches; and we shall see that in the other branch the mercury will be raised to 84 inches above it, which with the 28 of the weight of the atmosphere makes 112, a number four times 28, just as the first extent of 12 inches is four times the last extent of 3 inches.
To carry out these experiments successfully the small branch should have a section which is uniformly the same; but it is not necessary that the section of the long branch should be precisely the same in all its length.